autoconvolution equations and generalized mittag-leffler ‎functions

Authors

s. ‎eshaghi

a. ansari

abstract

this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of the inverse laplace transform, we use the schouten-vanderpol theorem to establish an autoconvolution equation for the generalized mittag-leffler functions in terms of the laplace and mellin transforms. also, in special cases we reduce the solutions of the introduced autoconvolution equations with respect to the volterra $mu$-functions. moreover, more new autoconvolution equations are shown using the laplace transforms of generalized mittag-leffler functions. finally, as an application of the autoconvolution equations in thermodynamic systems, we apply the laplace transform for solving the boltzmann equation and show its solution in terms of generalized mittag-leffler ‎functions.‎

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Autoconvolution equations and generalized Mittag-Leffler ‎functions

This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...

full text

Cascade of Fractional Differential Equations and Generalized Mittag-Leffler Stability

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

full text

Fractional differential equations for the generalized Mittag-Leffler function

*Correspondence: [email protected] 3Department of Mathematical Sciences, UAE University, Al Ain, United Arab Emirates Full list of author information is available at the end of the article Abstract In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involvin...

full text

Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations

and Applied Analysis 3 and define recursively a∇−nf t ∫ t a a∇−n 1f τ ∇τ 2.4 for n 2, 3, . . .. Then we have the following. Proposition 2.1 Nabla Cauchy formula . Let n ∈ Z , a, b ∈ T and let f : T → R be ∇-integrable on a, b ∩ T. If t ∈ T, a ≤ t ≤ b, then a∇−nf t ∫ t a ̂ hn−1 ( t, ρ τ ) f τ ∇τ . 2.5 Proof. This assertion can be proved by induction. If n 1, then 2.5 obviously holds. Let n ≥ 2 an...

full text

Evaluation of generalized Mittag-Leffler functions on the real line

This paper addresses the problem of the numerical computation of generalized Mittag–Leffler functions with two parameters, with applications in fractional calculus. The inversion of their Laplace transform is an effective tool in this direction; however, the choice of the integration contour is crucial. Here parabolic contours are investigated and combined with quadrature rules for the numerica...

full text

Mittag-Leffler Functions and Their Applications

Motivated essentially by the success of the applications of the Mittag-Leffler functions in many areas of science and engineering, the authors present, in a unified manner, a detailed account or rather a brief survey of the Mittag-Leffler function, generalized Mittag-Leffler functions, MittagLeffler type functions, and their interesting and useful properties. Applications of G. M. MittagLeffler...

full text

My Resources

Save resource for easier access later


Journal title:
international journal of industrial mathematics

Publisher: science and research branch, islamic azad university, tehran, iran

ISSN 2008-5621

volume 7

issue 4 2015

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023